Fluid Pressure Drop Research Articles

Off-design performance analysis of a new 300 MW supercritical CO2 coal-fired boiler

In order to solve existing problems of large working fluid pressure drop and lower reheated working fluid temperature under part load conditions, a new 300 MW S–CO2 coal-fired boiler heating surface arrangement is proposed and its off-design performances are studied. The new S–CO2 boiler adopts the single furnace double-tangential circle arrangement without the center wall and increases the proportion of reheat radiant heat exchange surfaces. The performance analysis model is built. The variations of the reheated working fluid temperature, working fluid pressure drop and the off-design performances of the boiler with the changes of coal type, excess air coefficient and operating load are investigated. The results show under the design load, the total pressure drop of working medium in the furnace is reduced by 0.48 MPa, under 30% of the design load, the reheated working medium temperature is increased by 7.62 °C, and the lower heating value and components of coal greatly influence the boiler efficiency. When the excess air coefficient is 1.2–1.4, the best efficiency zone is reached. The load range with the optimal efficiency zone is about 70%–100% of the design load. Achievement of this paper will provide valuable references for the design of the S–CO2 coal-fired boiler.

Micro-Channel Heat Sink: A Review

The method to cool a high heat flux device is an important research direction for the heat exchanger design. Micro-channels are an effective heat exchange structure both for single-phase and two-phase flow. In this paper, the heat transfer correlations of single-phase, two-phase and nanofluid in a micro-channel are discussed and analyzed. The correlations of pressure drop for single-phase and two-phase fluids are also presented. Excluding the different working fluids used in the micro-channel, the diameter and aspect ratio, shape and structure, surface roughness, internal and external factor and layout of micro-channel pipe are considered to analyze their influence on the heat transfer performance and pressure drop. Micro-channel technology applications include industry, air-conditioning, solar energy systems, heat pipe technology and computer data center cooling. Compared to the conventional heat exchangers used in these fields, a micro-channel heat sink showed a much better heat transfer coefficient and low volume, indicating that it is a good choice and has huge potential for cooling application. Finally, existing problems and future scopes are described, and drawing up design standard, experimental and simulated methods for evaluating its performance are the urgent actions which need to be carried out. This review paper serves as guidance for researchers to design and predict the performance of micro-channel heat sinks.

Laser Microtextured Surfaces for Friction Reduction: Does the Pattern Matter?

Frictional performances of different textures, including axisymmetric and directional patterns, have been tested in the mixed and the hydrodynamic lubrication regimes. Experimental results, corroborated by numerical simulations, show that the leading parameter is the geometrical pattern void ratio since a large number of dimples offers, at low speed, a trap for debris whereas, at high speed, due to the flow expansion in each micro-hole, fosters a fluid pressure drop, the consequent insurgence of micro-cavitation and, ultimately, the reductions of the shear stresses. Furthermore, in this paper, it is shown that, by means of directional textures, equivalent hydrodynamic wedges can be built up, thus establishing different friction performances depending on the flow direction.

Frictional melting and thermal fracturing recorded in pelagic sedimentary rocks of the Jurassic accretionary complex, central Japan

Deep ocean drilling revealed that shallow seismic slip in subduction zones is localized along weak pelagic clay, resulting in devastating tsunamis. However, the actual conditions of earthquake faulting in the deeper portions of subduction zones are largely unknown. The Jurassic chert–clastic complex in central Japan was formed under a cold subduction zone, within which the termination stage of superanoxia in the Middle Triassic was recorded in the pelagic sedimentary rocks. We conducted structural and Raman spectroscopic analyses of the fault rocks distributed along the thrust fault branched from the plate-boundary décollement. The results show that preferential melting of illite, thermal erosion, wall-rock fracturing, and increased carbonization are recorded along a few millimeter-thick pseudotachylyte derived from the black carbonaceous mudstone. A comparison of the clast volume fraction between the pseudotachylyte and black carbonaceous mudstone indicates that half amount of the clasts in the pseudotachylyte originate from the incorporation of fractured wall rocks composed of pelagic chert. Thermal modeling using the thermal diffusivities of wall rocks and the measurement of wall-rock fracture density suggest that fractured wall rocks represent thermal fracturing associated with the alpha–beta transition of quartz in the chert. Our pseudotachylyte study suggests that seismic slip at the deeper portions of the subduction zones is localized along the black carbonaceous mudstone flanked with chert. The intensely fractured wall rocks may be characteristic of pseudotachylyte, which accompanies quartz-rich wall rocks with high thermal diffusivities. The coseismic thermal fracturing of wall rocks potentially affects the dilatancy-induced fluid pressure drop in the slip zone and the reduction of wall-rock stiffness, resulting in the generation of frictional melt and acceleration of seismic slip.

On the influence of thermal phenomena during cavitation through an orifice

Thermal properties of cryogenic fluids can profoundly change the nature of cavitation since the fluid pressure drop is not, anymore, the only driving parameter of this phenomenon.In this research, we have conducted experiments inducing cavitation via a cylindrical orifice using Liquid Nitrogen as working fluid and exploring cavitation regimes going from bubbly cavitation to full flashing. Among others, we performed unsteady pressure measurements to derive the speed of sound during cavitation and high-speed imaging to understand the evolution of the two-phase flow along the pipe.In our analysis we use five dimensionless numbers to describe the flow conditions upstream and downstream of the orifice, and the type of transition taking place across the orifice.In this paper, we show that the fluid initial subcooling level ΔTsub upstream of the orifice and the superheat level Rp of the flow downstream of the orifice are two parameters essential to take into account the metastability of the fluid. Therefore, we propose a new semi-empirical model for predicting the effect of the fluid thermal properties on cavitation. Specifically, we define a parameter T which, multiplied by the saturation pressure at the inlet temperature, allows us to estimate the pressure reached at the orifice to cavitate.

Research on fluid flow mechanism of fracture-cave carbonate reservoirs based on fluid mechanics

ABSTRACT Facture-cave carbonate reservoir has not formed mature development theory and method up to now, and the development is world-class difficult problems, which are caused by that it is not clear to understand the particularity of reservoir characteristics and fluid flow mechanism. Because karst caves are the dominant reservoir space and production contributor, porous flow mechanics is not applicable. Reservoir body belongs to neither porous media nor continuum as a whole, hence fluid flow belongs to the research category of fluid mechanics. Contrary to widely adopted coupling method, this paper will focus on the fluid flow mechanism by only applying the theory of fluid mechanics and ignoring porous flow on the basis of analyzing the particularity of reservoir characteristics. Both capillary pores in carbonate matrix and slender dissolved cavities can be regarded as hydraulic long pipe, and fluid flow conforms to pipe flow law. Fluid flow in fracture belongs to parallel plate clearance differential pressure flow, which is similar to pipe flow. Fluid is static under gravity and fluid flow conforms to hydrostatics law in approximately equiaxed karst caves, and fluid flow out of karst cave is orifice outflow. Porous flow in reservoirs is unified with pipe flow. The essence of porous flow is the macro performance of pipe flow in countless capillary pores, which manifests as Darcy’s law under laminar condition. Porous flow in carbonate matrix can be completely ignored because it is extremely difficult to occur and the effect is very tiny. In dissolved-cavity reservoir body of millimeter scale, fluid flow is mainly slight pipe flow and gravity effect is significant, which leads to tiny production pressure differential and pressure drop funnel. In karst-cave reservoir body of meter scale, there is no fluid flow nor pressure drop in horizontal direction and the displacement of oil by water is piston-like displacement vertically upward in karst caves, hence pressure drop funnel does not exist at all. The production pressure differential generated by orifice outflow at the outlet of karst cave is very tiny and can be ignored. The new fluid flow mechanism based on fluid mechanics will provide theoretical basis for solving the difficult problems of developing fracture-cave carbonate reservoirs.

Second law thermodynamic analysis of imbalanced counter flow heat exchanger for energy conservation

Entropy generation of imbalanced counter flow heat exchanger is analyzed to know the thermal behavior effects such as entropy generation minimization and exergetic efficiency. The analysis of first law which does not considers different irreversibilities such as transfer of heat, drop in fluid pressure and mass flow streams unbalance is possible from second law of thermodynamics studies. In this analysis the parameters which are considered are length to diameter dimensions of heat transfer equipment tube, fluid streams capacity ratio, Reynolds number of fluid and type of fully developed fluid flow. To understand the behavior of heat exchanger the heat capacity rate of heat exchanger’s maximum value is changed for both cases of hot stream and cold stream. Optimum heat exchanger geometrical dimension namely length-to-diameter ratio can be obtained from the second law analysis corresponding to lower total entropy generation and higher second law efficiency which leads to energy conservation. Accordingly, for the minimum entropy generation and maximum exergetic efficiency resulted, the optimum length-to-diameter ratio are obtained for different cases considered.

Experimental Study on the Effect of Localized Blockages on the Friction Factor of a 61-Pin Wire-Wrapped Bundle

Abstract The thermal-hydraulic behavior of the flow in rod bundles has motivated numerous experimental and computational investigations. Previous studies have identified potential for accumulation of debris within the small subchannels of typical wire-wrapped assemblies with subsequent total or partial blockage of subchannel coolant flow. A test campaign was conducted to study the effects of localized blockages on the bundle averaged friction factor of a tightly packed wire-wrapped rod bundle. Blockages were installed within the bundle, and fluid pressure drop was measured across one wire pitch for a Reynolds number range of 500–17,200. The Darcy–Weisbach friction factor of the perturbed rod bundle geometry was compared with that of the unblocked bundle, as well as with the predictions of a well-established friction factor correlation. Differing effects based on blockage size and location for various flow regimes were studied. A number of conclusions can be made about the effects of the blockages on the friction factor, such as an increasing effect of the blockage on friction factor with an increase in Reynolds number, a change in flow behavior in the turbulent transition flow regime near Reynolds number 3000, differences in effect on friction factor for different types of subchannel blockage, and a nonlinear trend in friction factor variation with flow area impeded for edge subchannels. To this end, all data and quantified uncertainty produced in this study are made available for comparison and validation of advanced computational tools.

Design optimization, construction and testing of 2 K Joule-Thomson heat exchanger for a superfluid helium cryogenic system

The performances of 2 K Joule–Thomson (J-T) heat exchanger are related to the operation efficiency and economy of the superfluid helium cryogenic system, and the helically finned-tube heat exchanger (HFHE) is designed and tested. Heat transfer characteristics of the HFHE are investigated by a finite difference analysis method, and the design optimization of the HFHE is performed by the orthogonal test and variance analysis method. Meanwhile, the influences of the geometrical parameters on the performances are discussed. The experimental investigation of the HFHE is carried out in the superfluid helium cryogenic system, and the performances of the HFHE are verified experimentally. The results are shown that the calculated performances of the HFHE cause by heat transfer are in reasonable agreement with the experimental results, which indicates that the thermal calculation model of the HFHE is more accurate. Moreover, the deviations of pressure drop of cold fluid between the calculation and measurement are analyzed and the friction factor is modified in this paper.

Local multiphase flow characteristics of a severe-service control valve

For safety-critical industrial applications, severe-service valves are often used, and the conditions during operations can be either single phase or multiphase. The design requirements for valves handling multiphase flows can be very different to the single-phase flow and depend on the flow regime within valves. The variation in flow conditions during the operation of such valves can have a significant effect on performance, particularly in oil and gas applications where multiphase behaviour can rapidly change within the valve causing unwanted flow conditions. Current practices in designing and sizing such valves are based solely on global phase properties such as pressure drop of the bulk fluid across the valve and overall phase ratio. These do not take into account local flow conditions, as with multiphase fluids, the flow behaviour across the valve becomes more complex. In this work, a well-validated computational fluid dynamics (CFD) model is used to locally and globally quantify the performance characteristics of a severe service valve handling multiphase gas and liquid flow. Such flows are frequently encountered in process equipment found in vital energy industries e.g. process and oil & gas. The CFD model was globally validated with benchmark experiments. Two valve opening positions of 60% and 100% were considered each with 5, 10, and 15% inlet air volume fractions to simulate real life conditions. The results show that while the non-uniformity in pressure field is along expected lines, there is severe non-uniformity in the local air, water and void fraction distributions within the valve trim. To quantify the phase non-uniformities observed, an equation for the distribution parameter was defined and used to calculate its value in each localised quarter within the trim. Phase velocity and void fraction data extracted from the CFD results were also used to obtain relationships for the local void fraction distribution and flow coefficient. The detailed investigation that has been carried out allows for local flow characteristics to be determined and embedded in sizing methodology for severe-service control valve systems with multiphase gas and liquid flow.

Experimental estimation of axial–vertical flow permeability through a packed bed of granular activated carbon

Flow through packed beds of granular materials, and for instance, granular activated carbon (GAC), is of great importance and has various applications in desalination, refinery, filtration, separation, and so forth. Hence, transport analysis and flow characterization of such problems have to be supported by experimental data. In the present study, flow transport through a packed bed of GAC, as an adsorbent material, is analyzed experimentally. The focus of the work is on the axial–vertical flow of air and argon through five different GAC grain samples to characterize the flow behavior in terms of GAC grain size. In addition, some other affecting parameters, including the fluid inlet pressure and the flow rate, are studied and their effects on the permeability of the porous bed as well as fluid pressure drop are presented. To study the effects of the gravity on friction factor and pressure drop, all tests are performed in two situations—fluid flow with the same and the opposite direction as the gravitational acceleration. It is found that gravity can increase the pressure drop about 10 to 400 Pa (about 10 to 25% higher) which is significant. Also, the pressure drops through the packed bed of GAC are found and the results are reported in terms of non-dimensional parameters of friction factor versus Reynolds number, to propose proper correlations for various fluids flowing in different directions through the applied GAC grains. Correlations, which are reported in this article, can be used in designing systems in which pressure drop is of great importance, and activated carbon in the vertical situation is utilized.

Flow and heat transfer characteristics study of supercritical CO2 in horizontal semicircular channel for cooling process

Heat transfer and pressure drop characteristics of supercritical CO2 in horizontal semicircular channels was investigated numerically. Comparison study of flow and heat transfer characteristics of semicircular and circular channels at the same inlet velocity and mass flux was conducted respectively with the bulk temperature ranging from 27 °C to 67 °C. It is shown that the fluid heat transfer coefficient and pressure drop in the circular channel are slightly higher than those of the semicircular channel, but the fluid temperature drop through the circular channel is lower than that of the semicircular channel under the same hydraulic diameter. The effect of heat flux and channel hydraulic diameters on the heat transfer coefficient and pressure drop was analyzed for horizontal cooling semicircular channels. It is found that smaller hydraulic diameter enhances heat transfer, but the channel flow resistance increases significantly. The numerical results also indicate that the pressure drop decreases with the increase of heat flux, and the heat transfer coefficients depend on both bulk temperature and cooling heat flux.

Hydro-thermal performance of CNT nanofluid in double backward facing step with rotating tube bundle under magnetic field

In this study, a novel method for convective heat transfer control of flow past a double backward facing step with combined effects of oriented magnetic field, rotating tube bundle and inclusion of highly conductive CNT nanoparticles in the base fluid is offered. Hydro-thermal performance assessment of double backward facing step is numerically performed with finite volume method in laminar flow regime. Effects of Reynolds number, rotational Reynolds number, circular cylinder arrangement and horizontal local of the tube bundle, distance between the steps and magnetic field strength on the fluid flow, heat transfer, pressure drop and hydro-thermal performance coefficient variation are examined. The rotation of the cylinder, arrangement and location were found to alter hydro-thermal performance while the average Nu is enhanced with higher Reynolds and Hartmann numbers. The presence of the upper vortex location resulted in higher deflection of the main stream toward the hot bottom wall which resulted in higher local heat transfer rates. This is especially the case for clockwise direction rotation at the height speed and local Nu value increment is 244% as compared to non-rotating cylinder case. Best performance coefficient is obtained with MHD flow at Hartmann number of 5 while performance increase is 13% as compared to non-magnetic field configuration. The vertical size and location of the upper vortex changes with the horizontal location of the tube bundle and spacing between the steps. As compared to reference configurations, variations in the hydrothermal performance coefficients are 15% and 20% when varying the horizontal location and distance between the steps. The CNT nanoparticles inclusion in the base fluid resulted in performance coefficient enhancement of 52% at the highest solid volume fraction. As flow separation and subsequent attachments are encountered in a variety of heat transfer engineering applications, the results of the present work will be helpful in the design and optimization of various thermal engineering systems.

Pressure Drop and Film Thickness of Liquid-Liquid Taylor Flow in Square Microchannels

The fluid flow and pressure drop of liquid-liquid Taylor flow in a square microchannel are studied, both experimentally, and numerically using a three-dimensional numerical simulation. The experiments were carried out with a square channel having a hydraulic diameter of 2 mm, and the numerical simulations were performed for square channels with hydraulic diameters of 1 and 2 mm. The working fluids were water droplets in a hexadecane or kerosene carrier fluid. The droplet shape, droplet velocity, film thickness and pressure drop of the liquid-liquid Taylor flows were studied over Reynolds number and Capillary number ranges of 6 ≤ Re ≤ 100 and 0.0005 ≤ Ca ≤ 0.02 respectively. It was found that the droplet velocity and the geometry of the front and rear of the droplet are independent of the droplet volume. The droplet velocity was found to be approximately 10% higher than the mixture velocity for 0.0005 < Ca < 0.02. Correlations have been developed to predict the film thickness and pressure drop of liquid-liquid Taylor flow in square microchannels.

Determining the pressure drop of cemented Gobi sand and tailings paste backfill in a pipe flow

The pressure drop in pipes is a crucial parameter for the design of mine backfill. The friction factor correlations used to predict the pressure drop have not been validated for mine backfill. Therefore, this study presents a flow loop test to estimate the pressure drop based on a practical engineering case of cemented Gobi sand and tailings paste backfill (CGTPB). We employed two friction factor models for the pressure drop calculations in order to compare and validate our proposed test. Moreover, the effects of the CGTPB mixing components (solid mass concentration, binder content, and Gobi sand/tailings ratio) on pressure drop were investigated. Results demonstrate that the Swamee–Aggarwal model is able to effectively predict the pressure drop for Bingham plastic fluids that exhibit a laminar flow within the pipe. Furthermore, the pressure drop increases with concentration and binder content. The gel hydration product provides a lubricating effect that significantly reduces the pressure drop at a greater rate compared to the non-cementitious slurry. In addition, higher combined aggregate packing and slurry bulk densities will increase the pressure drop. The findings from our study contribute strongly to the mine backfill practice.

Sustainable densification of the deep crust

Abstract The densification of the lower crust in collision and subduction zones plays a key role in shaping the Earth by modifying the buoyancy forces acting at convergent boundaries. It takes place through mineralogical reactions, which are kinetically favored by the presence of fluids. Earthquakes may generate faults serving as fluid pathways, but the influence of reactions on the generation of seismicity at depth is still poorly constrained. Here we present new petrological data and numerical models to show that in the presence of fluids, densification reactions can occur very fast, on the order of weeks, and consume fluids injected during an earthquake, which leads to porosity formation and fluid pressure drop by several hundreds of megapascals. This generates a mechanically highly unstable system subject to collapse and further seismic-wave emission during aftershocks. This mechanism creates new pathways for subsequently arriving fluids, and thus provides a route for self-sustained densification of the lower crust.

Numerical Analysis of Complex Fracture Propagation Under Temporary Plugging Conditions in a Naturally Fractured Reservoir

Summary Temporary plugging during fracturing operations has become an efficient method to create a complex fracture network in tight reservoirs with natural fractures (NFs). Accurate prediction of the network-propagation process plays a critical role in plugging- and fracturing-parameter optimization. In this paper, the interaction between one single hydraulic fracture (HF) within a temporary plugging segment and multiple NFs was simulated using a complex fracture-development model. A new opening criterion for an NF penetrated by a nonorthogonal HF already was implemented to identify the dominant propagation direction of a HF under plugging conditions. Fracture displacements and the induced-stress field were determined by the 3D displacement-discontinuity method, and the Gauss-Jordan and Levenberg-Marquardt methods were combined to handle the coupling between rock mechanics and fluid flow numerically. Numerical results demonstrate that the opening and development of an NF are mainly dominated by its approaching angle and relative location. For a certain NF crossed by an HF within the plugging segment, the HF tends to propagate along the NF branch inclined in the main HF direction. The farther the interaction position is away from the HF tip, the easier the NF with an approaching angle less than 30° or larger than 150° can be open, and the outcome will be opposite if the approaching angle is larger than 45° or less than 135°. Higher approaching angle and plugging strength is necessary for expanding the position scope of NF that can be opened around HF. Under the effect of plugging, fluid pressure in the HF plummets at the beginning of the NF opening and keeps decreasing until the NF extends for a certain distance or encounters secondary NFs. Fluid-pressure drop occurs mainly in the unturned NF, together with the width of unturned NF being significantly lower than that of the turned NF and HF. Sensitivity analysis shows that the main factors, such as geometry, aperture profile, and fluid-pressure distribution, affecting the network progress under the temporary plugging conditions are the horizontal differential stress, NF position, approaching angle, plugging time, and plugging-segment length. The simulation results provide critical insight into complex fracture-propagation progress under temporary plugging conditions, which should serve as guidelines for well choosing and plugging optimization in temporary plugging fracturing.

Experimental and numerical investigation of convection heat transfer in a circular copper tube using graphene oxide nanofluid

To able to employ nanofluids in engineering applications, it is essential to investigate heat transfer properties in addition to thermophysical characteristics. In this work, the convection heat transfer coefficient of graphene oxide-distilled water nanofluid along a circular copper tube having a constant heat flux at the outside surface has been investigated both numerically and experimentally under turbulent flow regime. While the nanofluid convection heat transfer and head loss of pressure have been evaluated in the experimental section, the tube wall surface temperature, the convection heat transfer coefficient and friction factor have been obtained by using finite volume method in the numerical part with a three-dimensional domain by assuming single-phase flow. Surface and fluid temperatures and pressure drop of the distilled water have been acquired and compared with the related output from the correlation. Besides, the variations of the tube surface temperatures and the convection heat transfer coefficients of the nanofluids have been examined as numerical and experimental comparisons. The contours of the temperatures, convection heat transfer coefficients and pressure distributions for fluids have been presented. The convection heat transfer performances of the nanofluids according to the different volumetric flow rates, concentrations and the heat flux values have been exhibited in this study. The heat transfer coefficient increment value for the nanofluid of 0.02 vol% concentration and with a flow rate of 1.5 l/min (Re = 5032) has been obtained as about 48% for 5073.244 W/m2 (350 W) heat flux according to the distilled water.

The near-tip region of a hydraulic fracture with pressure-dependent leak-off and leak-in

In this paper we consider the near-tip region of a fluid-driven fracture propagating in permeable rock. We attempt to accurately resolve the coupling between the physical processes – rock breakage, fluid pressure drop in the viscous fluid flow in the fracture and fluid exchange between the fracture and the rock – that exert influence on the hydraulic fracture propagation, yet occur over length scales often too small to be efficiently captured in existing coarse grid numerical models. We consider three fluid balance mechanisms: storage in the fracture, pore fluid leak-in from the rock into the fracture as the result of dynamic suction at the dilating crack tip, and fluid leak-off from the fracture into the rock as the fluid pressure in the fracture recovers with distance away from the tip. This process leads to the formation of a pore fluid circulation cell adjacent to the propagating fracture tip. We obtain the general numerical solution for the fracture opening and fluid pressure in the semi-infinite steadily propagating fracture model, while assuming that the hydraulic fracturing and pore fluids have the same properties. We fully characterise the solution within the problem parametric space and identify different regimes of the fracture propagation. We assess the impact of the pore fluid leak-in and the associated near-tip circulation cavity on the solution and explore limitations of the widely used, pressure-independent Carter’s leak-off model. The obtained solution could be potentially used as a tip element in the finite crack models (penny-shaped, Planar3D), provided that a fast numerical implementation is further elaborated.

Numerical investigation of heat and mass transfer of water—silver nanofluid in a spiral heat exchanger using a two-phase mixture method

This study numerically investigates the heat and mass transfer characteristics of water—silver nanofluid flowing in a spiral heat exchanger (HX) using the two-phase mixture model. The hot side of the HX is pure water at the temperature of 343 K and Re = 500, while the cold side is nanofluid with volume fraction up to 5% at 305 K and Re number ranging from 500 to 2000. The cold and hot tubes are concentrically twisted 3.5, 5.5 and 7.5 turns in order to explore the heat transfer effectiveness of the heat exchanger as a function of the spiral turns. The results indicate that increasing the volume fraction of nanoparticles, Re number and the number of turns increases the overall heat transfer coefficient, heat rate absorbed by the cold fluid and pumping power of the HX noticeably. The above-mentioned factors also improve the temperature stability of the input fluid along with the heat exchanger. The effectiveness of the HX decreases by increasing the Re number, the volume fraction of nanoparticles and turning rounds due to the greater pressure drop of the coolant fluid. At a constant Re number, increasing the volume fraction and number of turns enhances the NTU parameter to a great extent.